Method for dynamically predicting service life of large-tonnage support of large-span railway bridge

Abstract

The invention belongs to the field of bridge structure health monitoring, and discloses a method for dynamically predicting the service life of a large-tonnage support of a large-span railway bridge, and the method comprises the following steps: carrying out the online calculation of the slippage data of the large-tonnage support under various monitoring conditions based on a transmission mechanism analysis formula between the complex slippage of the large-tonnage support and the deformation of a main beam; identifying and dynamically updating a long-span railway bridge support sliding influence coefficient set on line by using the information of the first-class detection train and the corresponding sliding data; a continuously changing railway traffic flow is loaded to the coefficient set to quickly calculate the vehicle-caused support sliding behavior, and the monitored long-term temperature effect is superposed to reconstruct the long-term wear process of complete support sliding; and analyzing an unsteady wear process by using a time-varying reliability theory to realize dynamic prediction of the service life of the large-tonnage support. The dynamic prediction method for the service life of the large-tonnage support provides a reasonable guidance basis for operation and maintenance and service life prolonging of a large-span railway bridge.

Description

Technical Field

[0001] The invention belongs to the field of bridge structure health monitoring and relates to a method for dynamically predicting the service life of large-tonnage bearings of a large-span railway bridge. Background Art

[0002] With the expansion of the global railway network, the number of long-span railway bridges has increased rapidly. As an important transportation hub, they are designed with high redundancy and long service life to provide optimal vehicle-rail operation performance. Therefore, the degradation of replaceable parts with short service life is a controlling factor affecting the operation and maintenance quality of long-span railway bridges. Large-tonnage bearings are critical but fragile connecting components, and their main function is to transfer reaction forces and deformations from the superstructure to the substructure. Large-tonnage spherical steel bearings are widely used in long-span railway bridges due to their high rotational flexibility, strong bearing capacity, durability and reliable lateral restriction. Its transmission function is realized by slide plates made of high-performance materials, but the accumulated slip caused by high-density train impact and material degradation caused by environmental excitation can cause severe wear of the slide plates. Bearing wear will change the boundary conditions of the bridge structure, resulting in abnormal transmission, large additional force, and even bearing jamming, which directly affects the operation quality of long-span railway bridges. Therefore, life prediction of large-tonnage bearings is a crucial topic, and reasonable prediction results can provide reasonable maintenance decisions for long-span railway bridges and extend their service life.

[0003] According to the different bearing slip estimation methods, the existing bearing service life prediction methods can be divided into two categories: model-based and data-based. However, the existing methods have limitations when applied to large-tonnage bearings of long-span railway bridges. For the former, researchers load a combination of traffic flow and environmental loads onto the bridge model to simulate bearing slip (Li et al. 2020. "Wear evaluation on slide bearings in expansion joints based on cumulative displacement for long-span suspension bridge under monitored traffic flow."; Wu et al. 2024. "Control of longitudinal movement response of suspension bridges induced by passing trains using low-exponent fluid viscous dampers."). Although these model-based methods can consider the changing traffic flow when estimating bearing behavior, they face two major limitations in application: 1) The model calculation of long-span railway bridges involves complex dynamic coupling analysis, and it is difficult to predict the service life through reliability analysis that requires a large amount of sampling and loading; 2) The bridge boundary conditions are often simplified during modeling, making it difficult to characterize and track the real sliding behavior of large-tonnage bearings of long-span railway bridges.

[0004] Existing data-based methods can be divided into two categories: direct monitoring using longitudinal displacement meters and indirect estimation through vibration monitoring data. Initially, researchers used longitudinal displacement meters installed in the beam end area to directly monitor bearing slip to predict service life (Guo et al. 2015. “Displacement monitoring and analysis of expansion joints of long-span steel bridges with viscous dampers.”; Wang et al. 2018. “Safety evaluation of the wear life of high-speed railway bridge bearings by monitoring train-induced dynamic displacements.”). However, the direct monitoring method has the following shortcomings: 1) The train loads on long-span railway bridges have high amplitudes and high speeds, resulting in train-induced bearing slip components appearing in very high frequency bands. The sampling frequency of most current longitudinal displacement meters is insufficient to capture the complete train-induced component, resulting in an overestimation of service life; 2) According to the Fourier transform characteristics, noise exceeding the Nyquist frequency will be severely amplified in the differential process of the cumulative slip calculation, resulting in prediction errors.

[0005] In order to accurately capture the complete bearing sliding behavior, researchers proposed an indirect estimation method using vibration monitoring data (Wu et al. 2020. "Sliding life prediction of sliding bearings using dynamic monitoring data of bridges."; Wei et al. 2024. "Wear life prediction of sliding bearings based on multitype monitoring data of bridges."). However, there are three main limitations: 1) It is not suitable for large-tonnage spherical steel bearings that separate translation and rotation functions; 2) These methods rely on historical monitoring data and cannot estimate the bearing sliding behavior under the changing traffic flow in the future; 3) They are all derived from the simply supported beam model and are not suitable for large-span railway bridges with multi-span arrangements; 4) Its prediction accuracy is highly dependent on the integrity of the monitoring data, but during the operation of large-span bridges, data loss due to sensor failure often occurs. In short, the existing methods have limitations when applied to large-tonnage bearings of large-span railway bridges. They cannot provide accurate prediction results and make it difficult for engineers to obtain reasonable operation and maintenance basis.

[0006] In summary, overcoming the above-mentioned defects and proposing a dynamic prediction method for the service life of large-tonnage bearings of large-span railway bridges has important engineering significance. Summary of the invention

[0007] The present invention aims to propose a dynamic prediction method for the service life of large-tonnage bearings of large-span railway bridges, which can accurately estimate the long-term sliding behavior of multiple groups of large-tonnage bearings of multi-span and multi-line large-span railway bridges online, automatically evaluate the wear condition of the bearings, and predict the service life of the bearings under continuously evolving traffic flows.

[0008] The technical solution of the present invention:

[0009] A method for dynamically predicting the service life of large-tonnage bearings of large-span railway bridges, the steps are as follows:

[0010] Step 1: Classify the monitoring scenarios according to whether the sampling frequency of the longitudinal displacement meter installed at the bearing of the long-span railway bridge is greater than the load frequency, and calculate the bearing plate slip S according to different routes pl (t) and ball plate sliding S sp (t);

[0011] (1.1) If F s / 2≥v / L, indicating that the sampling frequency of the longitudinal displacement meter is sufficient, so the longitudinal displacement monitoring data represents the complete plate slip S pl (t), spherical slip S sp (t) is expressed as follows:

[0012]

[0013] Among them, F s represents the sampling frequency of the longitudinal displacement meter, v represents the vehicle speed, L represents the full bridge length, R represents the spherical radius of the spherical crown lining, and h i represents the height of the neutral axis of the main beam section at the position of the i-th support, and α(t) represents the ratio of the flexural plate slip to the rotational plate slip, which is expressed as follows:

[0014]

[0015] Among them, q n (t) represents the generalized coordinate of the nth-order main beam deflection;

[0016] (1.2) If F s / 2<v / L, indicating that the sampling frequency of the longitudinal displacement meter is insufficient. In this case, the vertical acceleration response a(x j ,t) quadratic integral calculation fitting deflection response y(x j ,t), expressed as follows:

[0017]

[0018] Where xj represents the longitudinal coordinate of the acceleration of the jth span, v(x j ,0) and y(x j ,0) represent the initial velocity and initial displacement at xj, t represents the time coordinate under the single vehicle passing condition, and t0 represents the duration of the single vehicle passing condition; then the deflection response y(x j ,t) to obtain the temporal and spatial distribution of the deflection of the whole bridge y(x,t); the plate slip S pl (t) and ball plate sliding S sp (t) are respectively expressed as follows:

[0019]

[0020] Among them, x Bi represents the longitudinal coordinate of the i-th support, L i represents the length of the i-th span;

[0021] Step 2: Based on the information of the first empty train of the day and its corresponding bearing slip behavior data, online identification and dynamic update of the bearing plate slip influence coefficient set Φ pl,set and the ball plate sliding influence coefficient set Φ sp,set , the solution formula is as follows:

[0022]

[0023] Where ε = pl or sp, pl and sp represent the plate and spherical plate respectively, λ represents the regularization coefficient determined by the L-curve criterion, H represents the regularization matrix, S ε represents the bearing plate slip and ball plate slip vectors calculated based on the longitudinal displacement monitoring data and step 1 when the first empty train passes the bridge, and A represents the pre-calibrated first empty train information matrix;

[0024] Step 3: Virtually load the evolving traffic flow on the influence coefficient set to predict the vehicle-induced slip behavior, and reconstruct the bearing daily slip behavior by superimposing the temperature effect; fit the bearing daily cumulative slip distribution in each year;

[0025] (3.1) Virtual loading traffic flow To predict vehicle-induced slip behavior It is expressed as follows:

[0026]

[0027] (3.2) Solve multiple samples of various working conditions to calculate the wear equivalent coefficient η and fit the distribution, which is expressed as follows:

[0028]

[0029] in, and Represent the first derivative of the vehicle actuation force and quasi-static slip component with respect to time;

[0030] (3.3) Under a single vehicle passing condition, the reconstructed bearing accumulates vehicle-induced slip It is expressed as follows:

[0031]

[0032] Among them, ξ represents the main beam damping ratio;

[0033] (3.4) Daily cumulative slip of bearing It is expressed as follows:

[0034]

[0035] Among them, TD and ND represent the time when trains cross the bridge and the time when no trains cross the bridge respectively; S ε,t (t) represents the temperature effect monitored by the longitudinal displacement meter, which is extracted by processing the data with a sliding average filter with a window length set to 1 / 20 of the data length;

[0036] (3.5) Fitting the distribution of daily cumulative slip of the bearing in each year

[0037] Step 4: Predict the dynamic service life of large-tonnage bearings of large-span railway bridges based on time-varying reliability theory;

[0038] (4.1) Reliability index β of large-tonnage bearing degradation process ε (T) represents the following:

[0039]

[0040] Where [CS] represents the cumulative slip limit that the slide plate can withstand; CS ε,h represents the historical accumulated slip, obtained through historical data, and the missing historical data segments are reconstructed using steps 2 and 3;

[0041] (4.2) Service life of large tonnage bearings T w Prediction, expressed as follows

[0042]

[0043] Where T represents the service time; [β] represents the target reliability, which is 3.95.

[0044] Beneficial effects of the present invention:

[0045] 1) The present invention establishes the transmission mechanism analytical relationship between the deflection-induced plate slip, rotation-induced plate slip and ball plate slip in large-tonnage bearings and the deformation of the main beam of a large-span railway bridge. On this basis, an online calculation program that is not restricted by sensor type or structural form is developed to estimate the slip behavior of large-tonnage bearings in various monitoring scenarios. Therefore, the complete and accurate slip behavior of multiple large-tonnage bearings of large-span railway bridges can be automatically captured and used for their wear condition assessment and service life prediction.

[0046] 2) The present invention proposes a method for dynamically updating the influence coefficient set based on periodic monitoring and online tracking of the behavior of large-tonnage bearings of multi-line large-span railway bridges. The long-term bearing slip behavior is automatically reconstructed by loading the evolving railway traffic flow on the updated coefficient set and superimposing the monitored temperature effect. Then, the non-stationary bearing slip behavior is analyzed based on the time-varying reliability theory, and the dynamic service life prediction of large-tonnage bearings of large-span railway bridges under continuously evolving traffic flows is realized. In addition, this avoids the process of numerically simulating the bearing slip behavior using a large-scale train-track-bridge coupling model and expensive manual inspections that require bridge closures, thereby significantly improving the prediction efficiency and economy.

[0047] 3) The present invention has been successfully applied to a certain in-service long-span railway bridge equipped with typical large-tonnage bearings. First, the sliding behavior of the target bearings within two years was accurately reconstructed and verified by estimation based on vibration monitoring. Then, the service life of three groups of large-tonnage bearings under different railway traffic flows was automatically predicted, including changes in train numbers, vehicle types and bridge functions. The application results show that the service life prediction results of the target bearings under different traffic flows vary greatly; but they all meet the design service life requirements and remain in good service condition. This method provides reasonable guidance for the maintenance and life extension of bearings of large-span railway bridges, has important engineering significance and practical value, and also contributes to sustainable development. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Flow chart of the method of the present invention.

[0049] Figure 2 Schematic diagram of a real bridge in the implementation of the method of the present invention, wherein (a) is the bridge structure and sensor arrangement, and (b) is the line and support arrangement.

[0050] Figure 3 The sliding behavior influence coefficient set of the target support in the implementation of the method of the present invention, wherein (a) is the sliding influence coefficient set of the plate, and (b) is the sliding influence coefficient set of the ball plate.

[0051] Figure 4The traffic flow and wear equivalent coefficient distribution in the method of the present invention, wherein (a) is the train number, (b) is the train car mass, and (c) is the wear equivalent coefficient.

[0052] Figure 5 It is the daily cumulative slip distribution of the target bearing in the implementation calculation of the method of the present invention, wherein (a) is the daily cumulative plate slip distribution, and (b) is the daily cumulative train car mass distribution.

[0053] Figure 6 The service life prediction results of the target bearing in the implementation of the method of the present invention are shown in FIG. 1 , wherein (a) is the service life of the plate and (b) is the service life of the ball plate. DETAILED DESCRIPTION

[0054] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0055] The present invention proposes a method for dynamically predicting the service life of large-tonnage bearings of large-span railway bridges, which includes "classifying monitoring scenarios according to whether the sampling frequency of the longitudinal displacement meter is greater than the load frequency and calculating the bearing plate slip and ball plate slip", "online identification and dynamic updating of the influence coefficient set of bearing plate slip and ball plate slip based on the information of the first empty train of the day and its corresponding bearing slip behavior data", "predicting the vehicle-induced slip behavior by virtually loading the continuously evolving traffic flow on the influence coefficient set, and reconstructing the bearing daily slip behavior by superimposing the temperature effect, and then fitting the daily cumulative slip distribution of the bearing in each year", and "dynamically predicting the service life of large-tonnage bearings of large-span railway bridges based on time-varying reliability theory". The specific process has been given above, and the use and features of the present invention are explained next in conjunction with a real bridge example.

[0056] Example: Two-year monitoring data of a large-span steel truss arch high-speed railway bridge in service in China

[0057] The bridge structure and sensor layout of the bridge are as follows: Figure 2 As shown in (a), the bridge has six spans with a span arrangement of (108+192+2×336+192+108) meters. The main span is 336 meters long and uses double continuous steel trusses and continuous steel truss arches. The line and support arrangements are shown in Figure 2 As shown in (b), the bridge has six lanes, two high-speed train lanes on the downstream side, with a train speed of 250 km / h; two high-speed train lanes on the upstream side, with a train speed of 200 km / h; and two non-operating subway lanes on the outer side of the truss. The north side support of the north main span of the bridge is taken as the prediction target.

[0058] The sampling frequency of the longitudinal displacement meter on this bridge is not sufficient to collect the complete slip. Therefore, the vertical acceleration data in each span is quadratically integrated over time to obtain the deflection time history and cubic spline interpolation is performed to obtain the temporal and spatial distribution of the deflection. The method in step 1 (1.2) is used to calculate the slip of the large-tonnage bearings.

[0059] Using the first empty train condition every day within two years, the plate slip and ball plate slip influence coefficient set of the target bearing are calculated using the method proposed in step 2, and the annual average value is calculated, as follows: Figure 3 (a) and (b) are shown. The distribution of traffic flow and wear equivalent coefficients obtained by virtual addition statistics on the slip influence coefficient set (such as Figure 4 (a), (b) and (c), and the specific statistical characteristics are shown in Table 1) to reconstruct and fit the target support daily cumulative slip distribution in each year, as shown in Figure 5 As shown in (a) and (b).

[0060] Then, different traffic flow evolution cases were set up, and the service life of large-tonnage bearings of long-span railway bridges was automatically predicted based on the proposed method. The results are as follows: Figure 6 (a) and (b), see Table 2 for details.

[0061] Table 1 Statistical characteristics of railway traffic flow and wear equivalence coefficient

[0062]

[0063]

[0064] Note: DX refers to the single-car condition of a train passing through X carriages downstream, UX refers to the single-car condition of a train passing through X carriages upstream, and Double refers to the double-car condition.

[0065] Table 2 Life prediction results of large-tonnage bearings of target large-span railway bridges (unit: year)

[0066]

[0067]

Claims

1. A dynamic prediction method for the service life of large-tonnage bearings of large-span railway bridges, characterized in that: Here are the steps: Step 1: Classify the monitoring scenarios according to whether the sampling frequency of the longitudinal displacement meter installed at the bearing of the long-span railway bridge is greater than the load frequency, and calculate the bearing plate slip S according to different routes pl (t) and ball plate sliding S sp (t); Step 2: Based on the information of the first empty train of the day and its corresponding bearing slip behavior data, online identification and dynamic update of the bearing plate slip influence coefficient set Φ pl,set and the ball plate sliding influence coefficient set Φ sp,set ; Step 3: Virtually load the evolving traffic flow on the influence coefficient set to predict the vehicle-induced slip behavior, and superimpose the temperature effect to reconstruct the bearing daily slip behavior; Fit the daily cumulative slip distribution of the bearings in each year; Step 4: Predict the dynamic service life of large-tonnage bearings of large-span railway bridges based on time-varying reliability theory.

2. The method for dynamically predicting the service life of large-tonnage bearings of large-span railway bridges according to claim 1 is characterized in that: The specific steps of step one are as follows: (1.1) If F s / 2≥vL, indicating that the sampling frequency of the longitudinal displacement meter is sufficient, so the longitudinal displacement monitoring data represents the complete plate slip S pl (t), spherical slip S sp (t) is expressed as follows: Among them, F s represents the sampling frequency of the longitudinal displacement meter, v represents the vehicle speed, L represents the full bridge length, R represents the spherical radius of the spherical crown lining, and h i represents the height of the neutral axis of the main beam section at the position of the i-th support, and α(t) represents the ratio of the flexural plate slip to the rotational plate slip, which is expressed as follows: Among them, q n (t) represents the generalized coordinate of the nth-order main beam deflection; (1.2) If F s / 2<vL, indicating that the sampling frequency of the longitudinal displacement meter is insufficient. In this case, the vertical acceleration response a(x j ,t) quadratic integral calculation fitting deflection response y(x j ,t), which is expressed as follows: Where xj represents the longitudinal coordinate of the acceleration of the jth span, v(x j ,0) and y(x j ,0) represent the initial velocity and initial displacement at xj, t represents the time coordinate under the single vehicle passing condition, and t0 represents the duration of the single vehicle passing condition; then the deflection response y(x j ,t) to obtain the temporal and spatial distribution of the deflection of the whole bridge y(x,t); the plate slip S pl (t) and ball plate sliding S sp (t) are respectively expressed as follows: in, represents the longitudinal coordinate of the i-th support, L i Represents the length of the i-th span.

3. The method for dynamically predicting the service life of large-tonnage bearings of large-span railway bridges according to claim 1 is characterized in that: The specific steps of step 2 are as follows: Plate slip influence coefficient set Φ pl,set and the ball plate sliding influence coefficient set Φ sp,set , the solution formula is as follows: Where ε = pl or sp, pl and sp represent the plate and spherical plate respectively, λ represents the regularization coefficient determined by the L-curve criterion, H represents the regularization matrix, S ε represents the bearing plate slip and ball plate slip vector calculated based on the longitudinal displacement monitoring data and step 1 when the first empty train passes the bridge, and A represents the pre-calibrated first empty train information matrix.

4. The method for dynamically predicting the service life of large-tonnage bearings of large-span railway bridges according to claim 1 is characterized in that: The specific steps of step three are as follows: (3.1) Virtual loading traffic flow To predict vehicle-induced slip behavior It is expressed as follows: (3.2) Solve multiple samples of various working conditions to calculate the wear equivalent coefficient η and fit the distribution, which is expressed as follows: in, and Represent the first derivative of the vehicle actuation force and quasi-static slip component with respect to time; (3.3) Under a single vehicle passing condition, the reconstructed bearing accumulates vehicle-induced slip It is expressed as follows: Among them, ξ represents the main beam damping ratio; (3.4) Daily cumulative slip of bearing It is expressed as follows: Among them, TD and ND represent the time when trains cross the bridge and the time when no trains cross the bridge respectively; S ε,t (t) represents the temperature effect monitored by the longitudinal displacement meter, which is extracted by processing the data with a sliding average filter with a window length set to 1 / 20 of the data length; (3.5) Fitting the distribution of daily cumulative slip of the bearing in each year 5. The method for dynamically predicting the service life of large-tonnage bearings of large-span railway bridges according to claim 1 is characterized in that: The specific steps of step 4 are as follows: (4.1) Reliability index β of large-tonnage bearing degradation process ε (T) represents the following: Where [CS] represents the cumulative slip limit that the slide plate can withstand; CS ε,h represents the historical accumulated slip, obtained through historical data, and the missing historical data segments are reconstructed using steps 2 and 3; (4.2) Service life of large tonnage bearings T w Prediction, expressed as follows Where T represents the service time; [β] represents the target reliability, which is 3.95.

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